Shift of the condensation temperature caused by weak repulsion
In plain words
Weak repulsion between bosons raises their condensation temperature slightly, in proportion to the interaction strength. The coefficient is known only from computer simulations.
Precise statement
For the dilute 3D Bose gas, prove that $(T_{c} - T_{c}^{0})/T_{c}^{0} = c\rho^{1/3}a + o(\rho^{1/3}a)$, with $T_{c}^{0}$ the ideal-gas value, and determine c (lattice Monte Carlo gives c approximately 1.3, Arnold and Moore; Kashurnikov, Prokof'ev and Svistunov, 2001). Answer: the existence of the phase transition and the value of c.
What would settle it
A proof of a phase transition at $T_{c}$ with rigorous bounds on $c$.
Parent problems
- Special case of Condensation of a repulsive Bose gas in the thermodynamic limit · open · from revision 1 The parent was revised since revision 1: it now states another question.
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